power

Arguments

A,t

scalar, polynomial or rational matrix.

b

a scalar, a vector or a scalar matrix.

Description

• If A is a square matrix and b is a scalar then A^b is the matrix A to the power b.

• If b is a scalar and A a matrix then A.^b is the matrix formed by the element of A to the power b (element-wise power). If A is a vector and b is a scalar then A^b and A.^b performs the same operation (i.e. element-wise power).

• If A is a scalar and b is a matrix (or vector) A^b and A.^b are the matrices (or vectors) formed by a^(b(i,j)).

• If A and b are vectors (matrices) of the same size A.^b is the A(i)^b(i) vector (A(i,j)^b(i,j) matrix).

Notes:

- For square matrices A^p is computed through successive matrices multiplications if p is a positive integer, and by diagonalization if not.

- ** and ^ operators are synonyms.

Examples

A=[1 2;3 4];
A^2.5,
A.^2.5
(1:10)^2
(1:10).^2

s=poly(0,'s')
s^(1:10)

See Also

• exp — element-wise exponential
• hat — (^) exponentiation